{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# NumPy\n",
"\n",
"**Tomas Beuzen, September 2020**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These exercises complement [Chapter 5](../chapters/chapter5-numpy.ipynb) and [Chapter 6](../chapters/chapter6-numpy-addendum.ipynb)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercises"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import numpy under the alias `np`."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create the following arrays:\n",
"\n",
"1. Create an array of 5 zeros.\n",
"2. Create an array of 10 ones.\n",
"3. Create an array of 5 3.141s.\n",
"4. Create an array of the integers 1 to 20.\n",
"5. Create a 5 x 5 matrix of ones with a dtype `int`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use numpy to:\n",
"1. Create an 3D matrix of 3 x 3 x 3 full of random numbers drawn from a standard normal distribution (hint: `np.random.randn()`)\n",
"2. Reshape the above array into shape (27,)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create an array of 20 linearly spaced numbers between 1 and 10."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Run the following code to create an array of shape 4 x 4 and then use indexing to produce the outputs shown below."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"a = np.arange(1, 26).reshape(5, -1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"20\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[ 9, 10],\n",
" [14, 15],\n",
" [19, 20],\n",
" [24, 25]])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([ 6, 7, 8, 9, 10])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[11, 12, 13, 14, 15],\n",
" [16, 17, 18, 19, 20]])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[ 8, 9],\n",
" [13, 14]])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the sum of all the numbers in `a`."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 7."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the sum of each row in `a`."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 8."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Extract all values of `a` greater than the mean of `a` (hint: use a boolean mask)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 9."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Find the location of the minimum value in the following array `b`:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.0856306 , 0.99734545, 0.2829785 , -1.50629471, -0.57860025,\n",
" 1.65143654, -2.42667924, -0.42891263, 1.26593626, -0.8667404 ])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(123)\n",
"b = np.random.randn(10)\n",
"b"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 10."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Find the location of the maximum value in the following 2D array `c` (hint: there are many ways to do this question, but a quick search on stackoverflow.com will typically help you find the optimum solution for a problem, for example see [post](https://stackoverflow.com/questions/3584243/get-the-position-of-the-biggest-item-in-a-multi-dimensional-numpy-array)):"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-1.0856306 , 0.99734545],\n",
" [ 0.2829785 , -1.50629471],\n",
" [-0.57860025, 1.65143654]])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(123)\n",
"c = np.random.randn(3, 2)\n",
"c"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# Your answer here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solutions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import numpy under the alias `np`."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create the following arrays:\n",
"\n",
"1. Create an array of 5 zeros.\n",
"2. Create an array of 10 ones.\n",
"3. Create an array of 5 3.141s.\n",
"4. Create an array of the integers 1 to 20.\n",
"5. Create a 5 x 5 matrix of ones with a dtype `int`."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0. 0. 0. 0. 0.]\n",
"[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
"[3.141 3.141 3.141 3.141 3.141]\n",
"[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]\n",
"[[1 1 1 1 1]\n",
" [1 1 1 1 1]\n",
" [1 1 1 1 1]\n",
" [1 1 1 1 1]\n",
" [1 1 1 1 1]]\n"
]
}
],
"source": [
"print(np.zeros(5))\n",
"print(np.ones(10))\n",
"print(np.full(5, 3.141))\n",
"print(np.array(range(21)))\n",
"print(np.ones((5, 5), dtype=int))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use numpy to:\n",
"1. Create an 3D matrix of 3 x 3 x 3 full of random numbers drawn from a standard normal distribution (hint: `np.random.randn()`)\n",
"2. Reshape the above array into shape (27,)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[[-2.42667924, -0.42891263, 1.26593626],\n",
" [-0.8667404 , -0.67888615, -0.09470897],\n",
" [ 1.49138963, -0.638902 , -0.44398196]],\n",
"\n",
" [[-0.43435128, 2.20593008, 2.18678609],\n",
" [ 1.0040539 , 0.3861864 , 0.73736858],\n",
" [ 1.49073203, -0.93583387, 1.17582904]],\n",
"\n",
" [[-1.25388067, -0.6377515 , 0.9071052 ],\n",
" [-1.4286807 , -0.14006872, -0.8617549 ],\n",
" [-0.25561937, -2.79858911, -1.7715331 ]]])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.random.randn(3, 3, 3)\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-2.42667924, -0.42891263, 1.26593626, -0.8667404 , -0.67888615,\n",
" -0.09470897, 1.49138963, -0.638902 , -0.44398196, -0.43435128,\n",
" 2.20593008, 2.18678609, 1.0040539 , 0.3861864 , 0.73736858,\n",
" 1.49073203, -0.93583387, 1.17582904, -1.25388067, -0.6377515 ,\n",
" 0.9071052 , -1.4286807 , -0.14006872, -0.8617549 , -0.25561937,\n",
" -2.79858911, -1.7715331 ])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x.reshape(-1) # or x.reshape(27)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create an array of 20 linearly spaced numbers between 1 and 10."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 1.47368421, 1.94736842, 2.42105263, 2.89473684,\n",
" 3.36842105, 3.84210526, 4.31578947, 4.78947368, 5.26315789,\n",
" 5.73684211, 6.21052632, 6.68421053, 7.15789474, 7.63157895,\n",
" 8.10526316, 8.57894737, 9.05263158, 9.52631579, 10. ])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.linspace(1, 10, 20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below I've defined an array of shape 4 x 4. Use indexing to procude the given outputs."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1, 2, 3, 4, 5],\n",
" [ 6, 7, 8, 9, 10],\n",
" [11, 12, 13, 14, 15],\n",
" [16, 17, 18, 19, 20],\n",
" [21, 22, 23, 24, 25]])"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = np.arange(1, 26).reshape(5, -1)\n",
"a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"20\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[3,4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[ 9, 10],\n",
" [14, 15],\n",
" [19, 20],\n",
" [24, 25]])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 9, 10],\n",
" [14, 15],\n",
" [19, 20],\n",
" [24, 25]])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[1:,3:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([ 6, 7, 8, 9, 10])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 6, 7, 8, 9, 10])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[1,:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[11, 12, 13, 14, 15],\n",
" [16, 17, 18, 19, 20]])\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"array([[ 8, 9],\n",
" [13, 14]])\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 8, 9],\n",
" [13, 14]])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[1:3,2:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the sum of all the numbers in `a`."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"325"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 7."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the sum of each row in `a`."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 15, 40, 65, 90, 115])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.sum(axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 8."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Extract all values of `a` greater than the mean of `a` (hint: use a boolean mask)."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[a > a.mean()]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 9."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Find the location of the minimum value in the following array `b`:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.0856306 , 0.99734545, 0.2829785 , -1.50629471, -0.57860025,\n",
" 1.65143654, -2.42667924, -0.42891263, 1.26593626, -0.8667404 ])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(123)\n",
"b = np.random.randn(10)\n",
"b"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b.argmin()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 10."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Find the location of the maximum value in the following 2D array `c` (hint: there are many ways to do this question, but a quick search on stackoverflow.com will typically help you find the optimum solution for a problem, for example see [post](https://stackoverflow.com/questions/3584243/get-the-position-of-the-biggest-item-in-a-multi-dimensional-numpy-array)):"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-1.0856306 , 0.99734545],\n",
" [ 0.2829785 , -1.50629471],\n",
" [-0.57860025, 1.65143654]])"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(123)\n",
"c = np.random.randn(3, 2)\n",
"c"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Location of maximum: (2, 1)\n",
" Value of maximum: 1.65\n"
]
}
],
"source": [
"print(f\"Location of maximum: {np.unravel_index(c.argmax(), c.shape)}\")\n",
"print(f\" Value of maximum: {c.max():.2f}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}